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Show that the sum of an AP whose first t...

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a+c)(b+c-2a))/(2(b-a))`.

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EDUCART PUBLICATION-ARITHMETIC PROGRESSIONS-LONG ANSWER TYPE QUESTIONS
  1. The sum of four consecutive numbers in A.P. is 32 and the ratio of the...

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  2. Solve for x: 1+4+7+10+...+x=287

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  3. The sum of the first five terms of an A.P. and the sum of the first s...

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  4. Find the (i) sum of those integers between 1 and 500 which are multi...

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  5. Find the (i) sum of those integers between 1 and 500 which are multi...

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  6. Find the (i) sum of those integers between 1 and 500 which are multi...

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  7. An AP consists of 37 terms. The sum of the three middle most terms is ...

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  8. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  9. Find the sum of the integers between 100 and 200 that are divisible by...

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  10. Find the sum of the integers between 100 and 200 that are (i) divisi...

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  11. Which term of the AP : 21, 18, 15,... is 81? Also, is any term 0? Giv...

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  12. How many terms of the arithmetic progression 45, 39, 33,….. Must be ta...

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  13. Show that the sum of an AP whose first term is a, the second term b an...

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  14. If the sum of the first four terms of an AP is 40 and the sum of the f...

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  15. The sum of the 4^(th) and 8^(th) terms of an AP is 24 and the sum of i...

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  16. If the ratio of the 11^(th) term of an AP to its 18^(th) term is 2 : 3...

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  17. The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2). Show...

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  18. Solve the equation -4 + (-1) + 2 + … + x = 437.

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  19. A thief runs with a uniform speed of 100 m/min. After one minute a pol...

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  20. If the ratio of the sum of the first n terms of two Aps is (7n + 1) : ...

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